Developments in Ceramic Materials Research

122
José M. Rojo, José L. Mesa and Teófilo Rojo
has been also observed in some gadolinium and europium based compounds (S= 7/2), being
attributed to the filling-up of the 2S + 1 quantum energy levels [51,52]. Preliminary studies
using Mean Field Theory indicate that a shoulder superimposed onto the λ-type anomaly
appears for systems with S≥ 5/2 as in the case of Fe(PO3)3.
The thermal evolution of the magnetic entropy, Sm, for Cr(PO3)3 is shown in Figure 19, in
comparison with that of Mo(PO3)3. The total magnetic entropy for the chromium compound
was found to be 1.15 R, which agrees with the 83% of the theoretical value (1.39 R) for a S=
3/2 system. The small difference of the experimental entropy with respect to the theoretical
value could originate from the procedure to calculate the lattice contribution which is
approximate. Specific heat measurements of Cr2(P6O18) were not carried out due to its low
magnetic ordering temperature (at the limit of our experimental temperature range). However,
these ordering temperatures are accessible to neutron diffraction measurements which would
allow us to determine the magnetic structure of both metaphosphates and to better understand
the magnetic behavior of these compounds.
The total magnetic entropy, Sm= ∫(Cm/T)dT, was found to be 1.17R and 1.43R for the Mo
and Fe metaphosphates, respectively (Figure 20). These results agree with 84% of the
theoretical value (1.39 R) for an S= 3/2 system and 80% for an S= 5/2 (1.79R) (see Figure
20). An amount of 0.54R (47%) of the experimental entropy of Mo(PO3)3 was gained below
the ordering temperature, TN= 4 K, whereas in the case of Fe(PO3)3 the magnetic entropy
reaches 74% (1.06R) of the experimental entropy at the transition point. The value obtained
for the Mo phase is similar to that observed in other three-dimensional phosphate systems
where the entropy normally obtained near the Néel temperature reaches values of 1/3 of the
theoretical value [50]. The high value obtained for Fe(PO3)3 must be attributed to the
existence of magnetic anomalies as was previously described.
Sm (J/Kmol)
15
10
5
Sm teor = 1.39 R = 11.5 J/Kmol S = 3/2
Cr(PO 3 ) 3
T N
Mo(PO 3 ) 3
0
0 5 10 15 20 25 30 35
T(K)
Figure 19. Magnetic entropy of Cr(PO 3) 3 as a function of temperature together with that of Mo(PO 3) 3
for comparison. The horizontal solid line represents the theoretical Sm. The vertical solid line indicates
the ordering temperature.